BRUSSELS/PARIS (Reuters) - European Union ambassadors discussed on Wednesday possible new sanctions on Iran, diplomats said, under plans aimed at persuading U.S. President Donald Trump to preserve an international nuclear deal with Tehran.

The EU could decide to impose the extra measures under discussion in Brussels at a foreign ministers' meeting next month, four diplomats told Reuters.

Trump has given the European signatories a May 12 deadline to "fix the terrible flaws" of the 2015 nuclear deal, which was agreed under his predecessor Barack Obama, or he will refuse to extend U.S. sanctions relief on Iran.

Britain, France and Germany have proposed the extra EU sanctions over Iran's ballistic missile programs and its role in the war in Syria, according to a confidential document seen by Reuters. The hope is to encourage Trump to issue new waivers preventing those U.S. sanctions lifted under the deal from resuming next month.

One diplomat pointed to the next EU foreign ministers' meeting in Luxembourg on April 16. "The idea is to have a final decision on Iran sanctions by or at the April Foreign Affairs Council," the diplomat said.

The sanctions would not involve measures that were lifted under the nuclear deal but would instead target individual Iranians that the EU believes are behind Iran's ballistic weapons and its support for the government of Syrian President Bashar al-Assad, which is also subject to sanctions.

A list of names has been circulated to EU governments, a second diplomat said.

Any Iranians targeted would be subject to asset freezes and bans on traveling to the EU or doing business with companies based in the bloc.

EU envoys discussed possible sanctions on the basis of last week's meeting of foreign ministers in Brussels, who agreed that Iran needed to be held to account for its role in Syria's seven-year war, even while upholding the Iran nuclear accord.

At that meeting, France also urged the EU to consider new sanctions on Iran, citing publicly the "proliferation of ballistic missiles and (Tehran's) very questionable role in the near- and Middle East."

In response, France, Britain and Germany - the three European signatories to the nuclear deal - proposed new sanctions to fellow EU governments on March 16, although countries ranging from traditionally neutral Sweden and Ireland to Iran's closest European allies Italy and Greece still need to be convinced.

Any EU-wide measures would be the first significant punitive steps since the bloc lifted broad economic sanctions on Iran last year following the accord to curb Tehran's nuclear ambitions for at least a decade.

Another diplomat said discussions in EU capitals were moving in favor of new sanctions, partly after ballistic missiles fired by Yemen's Iran-backed Houthi militia killed a man in Riyadh on Sunday.